Winning the Unwinnable

by JRMayne 2 min read21st Jan 201054 comments


A few years back, I sent a note to some friends and other smart people. It said, approximately:

"I am trying to raise about $42 million. I have an expected payoff of about 20% in a week. It's not guaranteed; it might be more, or there could be a loss.

"Now, you may be saying to yourself, 'Mayne's got a system to win the lottery or something.'

"Well, it's not, 'something.' I have a system to win the lottery."

At which point I explained the system.

Now, LW is not particularly fond of the lottery. From a social policy/political point of view, I'm not disagreeing.

I specifically represent to you that I do have a system, I use a part of the system, and so far, I've lost about $350 with the system. If you'd loan me your $42 million when I ask for it, though, I'd have not only a high positive expectation, but a much smoother payout matrix, if I could solve the practical problem of buying as many tickets as I want. Which is 41.4 million tickets.

No, I'm not just saying I'll buy all the tickets and therefore guarantee the jackpot and therefore I win. I'm saying my expectation per dollar invested is substantially positive.

Skeptical? Why?

Not only do I have a system, but anyone with math skills and any knowledge of how the lottery works should agree. While it's always easy and obvious to see why other people should think the same as you, the fact that of a large number of math folks, zero here have defended playing the lottery as a cash-plus position, is a sign that people have foregone thinking and simply rejected the lottery outright. Or that I'm an idiot.

Before you get to the post payoff, what's your attitude toward this now? Lottery win is impossible? If you think it's impossible (or close enough to it), why? Unlikely? Probable? Would it change your mind if my self-assessment was that I was likely in the bottom quartile as far as current math skills on LW? Would it alter your probabilities if I told you that I am highly confident that if the practicality of buying 41.4 million tickets is worked out, that using my system to play the lottery is the best investment I know of?

OK, here it is: How to win the lottery.

I'm going to make this relatively brief, but it's really fairly simple. In California, we have a fairly classic lottery setup although the payout rates are a little worse than most states. The immediate payoff of the jackpot is about (carryover + 25% of tickets sold for that draw.) About 25% of the money into the lottery goes to non-jackpot payoffs. Fifty percent goes to valuable or less valuable government programs, including running the lottery.

You have about a 1 in 41 million shot of winning the jackpot with one ticket on any given draw.

A number of factors have seriously decreased purchases of Super Lotto tickets on large jackpots, primarily the cannibalization of the Lotto by the state's participation in the Mega Millions multi-state lottery. This is important to the calculations, and changes the expected payout substantially.

At one point, the Super Lotto jackpot was at $85 million for a prior draw (or $42.5 million in a single immediate payment) and they sold nine million tickets for the next draw.

So, consider: You put in $41.4 million and buy every possible ticket. You get about $10 million back in little prizes. The value of the jackpot is $42.5 million, plus 25% of nine million (the money the others put in) plus 25% of $41 million (the money you put in). You're at about $55 million in jackpot.

If no one ties you for the jackpot, you're at about $65 million in total payout. There's less than a 25% chance that someone ties you. That's a comfortable profit.

If one person ties you, that's about $37 million payout; that's a loss, but presumably a survivable loss. If more tie you that is, well, worse.

I came rather closer to pulling this off than seems likely; the big issue was how to buy the tickets, and the state told me I had to buy them from retailers (and I lack the political pull to find another way.) This opens a wide range of complications, as you can imagine. Then, sadly, some of the investment bankers of my acquaintance were, um, pursuing other interests (not because they were talking to some dude hawking a lottery system, or so I choose to believe), and the project dissolved.

But the math is still basically right. And the lottery has been repeatedly and forcefully brutalized here as something only idiots would play. When the cash expectation is positive, I'm playing again. I'm not saying it's stupid not to play - the marginal utility issues are substantial.

Still, by making the mental equation lottery=stupidity, a lot of people stopped thinking about the potential. I expect someone to pull this off some time, and I expect some political blowback (the lottery's for suckers, not the intelligent rich! What of the poor suckers?) Twenty million should make up for the blowback. Rationality is about winning, right?

Am I wrong on why this has been missed? Does this tell us anything about other opportunities that might be missed? Or, am I wrong that this should work, if the cash is present and the practical problems are solved? Or am I just an idiot?